In recent years, an x-ray mass estimation apparatus is used in which x-rays are irradiated to a measurement target object and the mass of the measurement target object is estimated (calculated) based on the amount of x-rays transmitted through the measurement target object.
With this x-ray mass estimation apparatus, an x-ray transmission image of the measurement target object is obtained, and then, by utilizing a characteristic that the image appears darker when the thickness of material in the x-ray transmission image is larger, the mass of the measurement target object is estimated according to the brightness per unit area included in the x-ray transmission image, for example, when the brightness is low, the mass is large, and when the brightness is high, the mass is small.
Specifically, given that the image brightness when there is no material is I0, the image brightness of a portion where x-rays are transmitted through material is I, and the thickness of material is t, a relationship among these factors is expressed by the following relational expression (1).I/I0=e−μt  (1)
Here, the value μ denotes a linear mass coefficient determined by x-ray energy and the type of material, indicating that the higher the value is, the greater the amount of x-rays that is absorbed.
Also, in order to estimate the thickness of the material from the brightness of the image, the following relational expression (2) is used.t=−1/μ×ln(I/I0)  (2)
In order to convert these values to the mass m, the following relational expression (3) is used in which an adequate coefficient is used as a multiplication factor.m=ct=−c/μ×ln(I/I0)=−α ln(I/I0)  (3)
(Note that the value “c” denotes a coefficient for converting the thickness of the material to the mass m)
Typically, an x-ray transmission image is formed by a plurality of pixels, thus it is possible to estimate the mass of the entire material by determining the mass m for each pixel and adding up these masses for the entire image. This can be expressed by the following formula (4).M=ΣΣm(x,y)  (4)
For example, in the Japanese Laid-Open Patent Application Publication No. 2002-296022 (published on Oct. 9, 2002), an x-ray mass estimation apparatus is disclosed, in which x-rays are irradiated to the measurement target object; x-rays transmitted therethrough are detected; the mass of the measurement target object is calculated per unit transmission area based on the amount of transmitted x-rays from a predetermined formula; and the calculated unit mass of the measurement target object per unit transmission area is integrated over the entire x-ray transmission area.